A Lagrangian Description of the Higher-Order Painlevé Equations

Abstract

We derive the Lagrangians of the higher-order Painlevé equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlevé test and satisfy the conditions stated by Jurá$\check{s}$, (Acta Appl. Math. 66 (2001) 25--39), thus allowing for a Lagrangian description.

16 pages, to be published in Applied Mathematics and Computation

References in corpus (4)

• Universality of a double scaling limit near singular edge points in random matrix models
• Non-autonomous Hénon-Heiles Systems
• The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation
• The Hamiltonian Structure of the Second Painleve Hierarchy